Calculate the wavelength of the spectral line obtained in the spectrum of li2+ ion the transition takes place between two - Chemistry - Structure of Atom

Question

Calculate the wavelength of the spectral line obtained in the
spectrum of li2+ ion the transition takes place between two levels
whose sum is 4 And difference is 2

Swati Krishna · Answer

x+ y = 4 {x= n1 & y= n2}
x-y = 2
2x = 6
x =3
y=1

1/wavelength = v` , wave no

v` = R (Z)^2 * [1/y - 1/x]
{R is rydbergs cnstnt
z = atomic no
y is taken first as electron move from lower to higher level}

v` = [109677 * (3)^2 * (1/1-1/3) ] cm^(-1)
{ z = 3}

v` = 109677* 9* 2/3
= 109677 * 6
= 658062 cm^(-1)

wavelength = 1/v`
= 1/ 658062 cm
it can also be converted to m
hop it hlpd

Calculate the wavelength of the spectral line obtained in the spectrum of li2+ ion the transition takes place between two levels whose sum is 4 And difference is 2

Let the transition occurs in between the levels n1​ and n2​. Thus, if then given n1​+n2​=4 n2​−n1​=2 ∴n2​=3,n1​=1 Therefore, λ1​=R​×Z2[121​−321​] (∵Z=3 for Li) =109678×32×[8/9] ∴λ=1.14×10−6cm

Let the transition occurs in between the levels n1 and n2. Thus, if then given
n1+n2=4
n2−n1=2 ∴n2=3,n1=1
Therefore, λ1=R×Z2[121−321] (∵Z=3 for Li)
=109678×32×[8/9]
∴λ=1.14×10−6cm